Logistic and Exponential Models

An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? 

• 101
• 102
• 103
• 104

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

If the number of bacteria in a colony doubles every 16 hours and there is currently a population of 3,000 bacteria, what will the population be 32 hours from now?

• 12,000 Bacteria
• 1.2 x 10¹³  Bacteria
• 196,608,000 Bacteria
• 6000 Bacteria

In an exponential function, what does the 'a' represent? 

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

h(x)= 12^{x
Find h(-2)}

• 1/144
• 1/24
• -144
• -24

g(x)=3(2)^{x
Find g(3)}

• 216
• 24
• 18
• 28

What is the equation of this table?

• y=512(1/4)^x
• y=32(4)^x
• y=32(1/4)^x
• y=512(4)^x

Des Moines is having a blizzard.  It has already snowed 1 inch and the total with double each hour.  Write an equation.

• y=1(2)^x
• y=1(1/2)^x
• y=2(1/2)^x
• y=2(2)^x

A bacterial colony doubles in size every 6 hours.  There are 90 bacteria present initially. Estimate the population size after 80 hours. What is the equation that models this problem?

• y= 90(2)^6/80
• y= 90(6)^80/2
• y= 2(90)^6/80
• y= 90(2)^80/6